摘要
若函数z=f(x,y)在点(x,y)处具有一阶连续偏导数fx(x,y),fy(x,y),则二元函数z=f(x,y)在点(x,y)处可微。2个偏导数fx(x,y),fy(x,y)都要求连续,条件相对比较苛刻。从该结论的证明过程分析得到了条件相对比较弱的可微性的充分条件:函数z=f(x,y)满足:在点P(x0,y0)处关于一个变量存在偏导数,关于另一个变量存在连续偏导数,则函数z=f(x,y)在点P(x0,y0)处可微。并将该结论推广到了n元函数。
If the function has continuous partial derivatives then the function is differentiable.But the condition that the two partial derivatives are continuous is very strict.In this paper,the weaker sufficient conditions for the differentiability about multivariate functions are discussed.The weaker sufficient condition for the differentiability is that if the function has continuous partial derivative about one variation,and has partial derivatives about another variation,then the function is differentiable.This conclusion is correct for multivariate functions with more than two variation.
出处
《长江大学学报（自科版）（上旬）》
CAS
2014年第1期19-20,2-3,共2页
JOURNAL OF YANGTZE UNIVERSITY (NATURAL SCIENCE EDITION) SCI ＆ ENG
基金
国家自然科学基金项目(11201039
61273179)
长江大学教学研究项目(JY2011023)
关键词
多元函数
可微性
偏导数
连续
Multivariate functions
differentiability
partial derivative
continuous
